K. Dajani

activity

20062026

most citedMultiple codings for self-similar sets with overlaps

16 citations · 51 across the 31 of their papers we have counts for

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28 papers · 1 filter

math.DS2026

A strange continued fraction associated with the Romik map

Yufei Chen, Karma Dajani, Yanyan Hu +1

In 2008, Dan Romik studied in this journal Primitive Pythagorean Triples, or PPTs. In order to do so, he introduced a modified slow (subtractive) Euclidean algorithm, and showed th…

math.DS2026

Coincidence of invariant measure for the alternate base transformations

Karma Dajani, Niels Langeveld

We characterize all pairs $(β, n), (β^{'}, m)$ such that the alternate $(β, n)$ and $(β^{'}, m)$ -transformations $K_{(β, n)}$ and $K_{(β^{'}, m)}$ have the same absolutely contin…

math.DS2024

Approximation properties of the intermediate $β$ -expansions

Karma Dajani, Yan Huang

Given $β > 1$ and $α \in [0, 1)$ , let $T_{β, α} (x) = β x + α (mod 1)$ . Then under the map $T_{β, α}$ each $x \in [0, 1]$ has an \emph{intermediate $β$ -expansion} of the form $x=\sum_{i=1}^\infty\…

math.DS2024

A new class of $α$ -Farey maps and an application to normal numbers

Karma Dajani, Cornelis Kraaikamp, Hitoshi Nakada +1

We define two types of the $α$ -Farey maps $F_{α}$ and $F_{α, ♭}$ for $0 < α < \frac{1}{2}$ , which were previously defined only for $\frac{1}{2} \leq α \leq 1$ by R.~Natsui (2004).…

math.DS2023★ 4 cited

A unifying theory for metrical results on regular continued fraction convergents and mediants

Karma Dajani, Cor Kraaikamp, Slade Sanderson

We revisit Ito's (\cite{I1989}) natural extension of the Farey tent map, which generates all regular continued fraction convergents and mediants of a given irrational. With a sligh…

math.DS2023

Ergodic properties of a parameterised family of symmetric golden maps: the matching phenomenon revisited

Karma Dajani, Slade Sanderson

We study a one-parameter family of interval maps ${T_{α}}_{α \in [1, β]}$ , with $β$ the golden mean, defined on $[- 1, 1]$ by $T_{α} (x) = β^{1 + ∣ t ∣} x - tβ α$ where $t \in {- 1, 0, 1}$ . For each $T…